When performing a hypothesis test on the population proportion, the test statistic is calculated as z=p*-p0/√(p0(1-p0))/n.
What is hypothesis?A hypothesis is an explanation proposed for a phenomenon. The scientific method requires that a hypothesis be testable in order for it to be considered a scientific hypothesis. Scientists typically base scientific hypotheses on previous observations that cannot be adequately explained by existing scientific theories. In a scientific context, a hypothesis (plural: hypotheses) is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon. A simple hypothesis is a statement that reflects the relationship between two variables. One is independent, while the other is dependent. Consider the statement, "Smoking is a leading cause of lung cancer." The independent variable, smoking, influences the dependent variable, lung cancer.
Here,
When conducting a hypothesis test concerning the population proportion, the value of the test statistic is calculated as z=p*-p0/√(p0(1-p0))/n.
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A thin strip of rubber has an unstretched length of14.9 PartAIf it is stretched around a pipe having an outer diameter of 5.0 in., determine the average normal strain in the stripExpress your answer using three significant figures.
We must first compute the length of the strip when it is wrapped around the pipe in order to establish the average normal strain in the strip.
The pipe has an exterior diameter of 5.0 inches, making its circumference:
Circumference = diameter * 5.0 inches * circumference = 15.7 inches
Since the rubber strip is stretched around the pipe, its length when stretched equals the pipe's circumference.
Stretched length equals 15.7 inches
Using the following formula, we can now get the strip's average normal strain:
strain is equal to (length changed / length at start)
strain is equal to (15.7 inches - 14.9 inches)/14.9 inches, which equals 0.0541 or 5.41%.
Therefore, the strip's average normal strain is 5.41%.
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Determine the terminal velocity of the block if the 0.1 mm gap between the block and the surface contains SAE 30 oil at60 °F (µ=0.38 N s/m²). Assume the velocity distribution in the gap is linear, and the area of the block in contact with the oil is 0.1 m²
The terminal velocity of the block if the 0.1 mm gap between the block and the surface contains SAE 30 oil at60 °F is 0.011 m/s.
To calculate the Reynold's Number (Re):
Re = (Vdρ)/μ
where V is the velocity of the block, d is the gap between the block and the surface, ρ is the density of the oil, and μ is the dynamic viscosity of the oil.
Re = (V×0.1×873)/(0.38)
To Calculate the Darcy-Weisbach friction factor (f):
f = 0.0047/Re^0.2
To calculate the terminal velocity of the block:
Vt = [2×f×L×g×ρ]/μ
where L is the length of the block in contact with the oil and g is the gravitational acceleration (9.8 m/s²).
Vt = [2*(0.0047/Re^0.2)×0.1×9.8×873]/0.38
Vt = 0.011 m/s
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Select the correct short description of a real object for which (Figure 1) would be a realistic position-versus-time graphO Eustace the truck driver had a load in a city 120 miles east of El Dorado. He drove west at Gomph for two hours to El Dorado where he spent an hour unloading the truck and loading up front cargo. He then drove backeasta 40gph for two hours to the final de cast of Dorado O Eustace the truck driver had a loadina cy 120 miles east of Dorado. He drove west at 60 mph for two hours to El Dorado where he spent two hours unloading the true and loading up forent cargo. He then drove west at 60 mph for two hours to the final destination 30 miles west of Dorado O Eustace the truck driver had a loadina 120 miles east of El Dorado. He drove west ato mph for two hours to El Dorado where he spent two hours unloading the truck and loading up different cargo. He then drove back cast at 40 mph for two hours to the final de miles east of Dorado O Eustacher had a d a y 120 east of El Dorado e dove where he spent an hour anger and leading up ort cargo. He then drove final destination miles west of El Dorado t ph for two hours Dorado
The constellation Dorado can be found in the southern sky is the correct short description of real object.
Dorado: what is it?
In the southern hemisphere, the constellation Dorado can be seen . One of the 88 constellations that are currently in existence, it was given a name toward the end of the 16th century. The dolphinfish (Coryphaena hippurus), more commonly referred to as dorado in Spanish, is referred to in the name despite being shown as a swordfish. The remaining portion of the Large Magellanic Cloud is in the constellation Mensa, with the majority of the cloud in the constellation Dorado. The South Ecliptic pole can also be found in this constellation.
Astronomers use the Latin genitive form Doradus to name its stars, giving the Spanish name Dorado; Together with the nearby asterism Argo Navis, it is thought to be a feminine proper name of Greek origin that ends in -. like Argo, Io, or Callisto).
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kim-lee founded a software development company at the age of 27. over time, he developed the company into a multibillion-dollar transnational organization. he is currently the chief technical officer of the company, holds 75 percent stock of the company, and makes major decisions regarding the products that would be made available to consumers. in the context of wright's model of the u.s. class structure, kim-lee belongs to the . group of answer choices capitalist class small-business class working class managerial class
social mobility, movement of individuals, families, or groups through a system of social hierarchy or stratification.
what is the transnational organization?
Transnational organization is a term used in scholarly literature. It refers to international organizations (usually, international nongovernmental organizations) that "transcend" the idea of a nation-state.Transnational corporations are one of the most important subjects of international economics. They are directly affecting new trends in international business, global competitiveness on international markets as well as economies of states, nations.The primary advantage of a transnational business strategy is that it is less costly than a multi-domestic strategy, as it prioritizes global standardization and efficiency. Transnational businesses centralize as many resources as possible, therefore cutting costs.To learn more about transnational refers to:
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The figure shows four particles, each of mass 30.0 g, that form a square with an edge length of d = 0.900 m. If d is reduced to 0.300 m, what is the change in the gravitational potential energy of the four-particle system?
The potential energy of the system have been observed as 0.7 J.
What is the change in the gravitational potential energy?We know that the potential energy is the energy that is possessed by an object that is found at a given height. The implication of this is that the potential energy depends on the height of the object.
If we decrease the height of the object then the potential energy of the body would also change. We have been told that the mass of the balls are 30 g each hence a total mass of 120 g or 0.12 Kg.
The change in the potential energy is;
0.12 * 9.8 * (0.9 - 0.3)
= 0.7 J
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Can anyone help me answer this question?
The density of gold is 19.3 g/cm^3. What is the value in kilogram per cubic meter? Show working.
19.3 gcm3 19.3 g c m 3 is equivalent to 19300 kgm3 due to the decimal place shifting due to the conversion being in metric measurements.
Density: What does that mean?The amount of objects, including people, animals, plants, and other living things, that are present in a region is known as the density. The number of objects is divided by the area to determine density. The number of inhabitants in a nation divided by its size, measured in square kilometers or miles, is the population density of that nation.
In its most basic form, what is density?In reference to the amount of matter contained in a thing, density refers to how much volume the object or substance occupies.
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a woodpecker beak has a velocity of 7.49 m/s at impact. if it stops in a distance of 1.87 mm, find the average acceleration of the woodpecker's beak
Answer:
Explanation: Average acceleration = (velocity/distance)
= Convert 1.87 to meters
1.87 / 1000 = 0.00187
(7.49 m/s / 0.00187 m)
= 3987.37 m/s²
A skydiver is falling at terminal velocity before opening her parachute. After opening her parachute, she falls at
a much smaller terminal velocity. How does the total upward force before she opens her parachute compare to
the total upward force after she opens her parachute?
(A) The ratio of the forces is equal to the ratio of the velocities.
(B) The upward force with the parachute will depend on the size of the parachute.
(C) The upward force before the parachute will be greater because of the greater velocity.
(D) The upward force in both cases must be the same.
In both scenarios, the upward force must be the same. Regardless of the speed, the force of air resistance equals your weight when you are falling with terminal velocity.
The drag force is inversely related to both the effective area of the falling object and the speed squared. The forces of gravity and drag are equal at terminal velocity. The effective area of the parachute substantially expands when it opens, greatly increasing the drag force. The stronger drag force causes the speed to decrease, which in turn causes the drag force to decrease until it and the force of gravity are once again in balance since the drag and gravity forces are no longer in balance.
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11.which one of the following graphs represent correctly the variation of maximum kinetic energy emax with the intensity of incident radiations having a constant frequency.
The supplementary diagrams, which represent option d, accurately show how maximum kinetic energy emax varies with intensity of incident radiations with constant frequency.
In physics, kinetic energy (KE) is the energy that an object has as a result of its motion. It is defined as the effort necessary to move a mass-based body from rest to the given velocity. Zero initial velocity is the state where an object is (u). The fundamental types of kinetic energy include electrical, acoustic, thermal, and radiant energy. Here is a quick glance at them. Radiant power is a type of electromagnetic energy. An event's repetitions per unit of time are what determine its frequency.
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predict the order of increasing electronegativity in each of the following groups of elements. (use < symbol to separate substances in the list.)
Electronegativity is a tendency of a atom/element to attract the pair of electrons.
B,O,Gaelectronegativity order = O>B>Ga
Mg,Ba,Caelectronegativity order = Mg>Ba>Ca
Ga,Al,Pelectronegativity order =P>Ga>Al
Al,O,Celectronegativity order =O>C>Al
When an atom of a certain chemical element forms a chemical bond, it has a propensity to draw shared electrons (or electron density). The atomic number and the separation of the valence electrons from the charged nucleus have an impact on an atom's electronegativity. An atom or a substituent group will draw electrons in greater amounts the higher the associated electronegativity. The sign and amplitude of a bond's chemical polarity, which characterizes a bond along the continuous scale from covalent to ionic bonding, can be quantitatively estimated using electronegativity. The inverse of electronegativity is electropositivity, which describes an element's propensity to accept valence electrons.
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when using a wheatstone bridge to measure resistance, values of resistance are used to determine the _____ of the meter circuit.
When using a wheatstone bridge to measure resistance, values of resistance are used to determine the galvanometer of the meter circuit.
What is Galvanometer ?One of the best tools for measuring electrical current is a galvanometer. To determine and quantify the strength and direction of electrical current in circuits, this device is utilised. The working principal of a moving coil galvanometer is that a coil carrying current placed in a magnetic field experiences a torque. The deflection is made sure to be proportional to the current strength by the coil springs and radial field. A galvanometer is not used in an AC bridge because the rotating torque depends on the average current flowing through the galvanometer's coils. However, there will be no average current flowing via the AC bridge. The magnetic field is influenced by the flow of electric current.
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the equivalent resistance of a circuit with one hundred 100-s resistors all connected in parallel combined with a series resistor of 1 s is ___.
The equivalent resistance of a circuit with one hundred 100-s resistors all connected in parallel combined with a series resistor of 1 s is 0.999Ω.
What is meant by resistor ?
A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device.A specified voltage can be supplied via resistors to an active device like a transistor.Modern resistors are often constructed from a carbon, metal, or metal-oxide layer.In these resistors, an insulating material is wrapped in a helix around a thin film of conductive (but still resistant) material.A passive electrical component called a resistor prevents the flow of electric current by introducing resistance.They are present in practically all electrical networks and electronic circuits. Ohms are used to measure resistance.To learn more about resistor refer to
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with what tension must a rope with length 3.00 m and mass 0.100 kg be stretched for transverse waves of frequency 42.0 hz to have a wavelength of 0.710 m ? activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type t
The equation of a transverse wave traveling on a rope is given by y=10sinπ(0. 01x−2. 000t) where y and x are in cm and t in seconds.
What is transverse waves?
A transverse wave is a wave in which particles move perpendicular to the direction of the wave propagation.A transverse wave is a type of progressive wave. The direction of propagation of a transverse wave is always perpendicular to its direction of vibration. Few specific types of transverse waves can travel through a vacuum. An electromagnetic wave or light wave is an example of a transverse.Hence a transverse wave of this nature is called a shear wave. Since fluids cannot resist shear forces while at rest, propagation of transverse waves inside the bulk of fluids is not possible. In seismology, shear waves are also called secondary waves or S-waves.
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An 80 kg astronaut takes a journey from the surface of Earth and lands on the surface of Mars. The acceleration due to gravity on Earth is 9.8 m/s² and
the acceleration due to gravity on Mars is 3.7 m/s².
How does the astronaut's mass and weight on Mars compare to their mass and weight on Earth?
Elimination Tool
Select one answer
A The astronaut's mass and weight on Mars will both be the same as they were on Earth.
B The astronaut's mass and weight on Mars will both be less than they were on Earth.
C The astronaut's weight on Mars will be the same as it was on Earth, but their mass will be less on Mars than it was on Earth.
D The astronaut's mass on Mars will be the same as it was on Earth, but their weight will be less on Mars than it was on Earth.
D) The astronaut's mass on Mars will be the same as it was on Earth, but their weight will be less on Mars than it was on Earth.
An object's mass is a measure of its amount of matter, and is independent of gravity. The astronaut's mass is 80 kg on both Earth and Mars.
Weight, on the other hand, is the force exerted on an object due to gravity and it is equal to the object's mass multiplied by the acceleration due to gravity.
So the weight of astronaut on Earth will be (80 kg)(9.8 m/s²) = 784 N and on Mars (80 kg)(3.7 m/s²) =296 N. As you can see, the weight of astronaut is less on Mars than it was on Earth.
Explanation:
Clearly A bc A is alwthe correct answer
You have 125 g
of a certain seasoning and are told that it contains 26.0 g
of salt. What is the percentage of salt by mass in this seasoning?
The percentage of salt by mass in this seasoning is 20.80%.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
You have 125 g of seasoning.
Amount of salt = 26.0 g
So, the percentage of salt by mass in this seasoning is = Amount of salt/total amount of seasoning× 100%
= 26.0 g / 125 g × 100%
= 20.80 %.
Hence, the percentage of salt by mass in this seasoning is 20.80%.
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What is the magnitude of the electric field at a point 2.0m from a point charge q=4.0nC? A.9N/CB.90N/CC.0.9N/CD.900N/C
The electric field has a 9 N/C magnitude.
In this case, we must find the size of an electric field resulting from a specific charge.
The idea of an electric field is taken from the reformulated version of Coulomb's law.
We'll employ the following formula:
E = 9 x 10 9 Nm2/C2 (q/r2), where q is the charge and C r is the charge's distance from the electric field, both expressed in coulombs.
R = 2 m for the information provided.
q = 4.0 nc = 4 x 10⁻⁹ C
E = ?
the problem's resolution
Use the following information to replace the formula for the electric field:
E=9x10-9 Nm2/C2 (q/r2)
E = 4 x 109 C / (2m)2 (4 x 109 N / m2)2
E = 9 N/C
As a result, the electric field's strength is 9 N/C in the direction of the charge.
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what are the strength and direction of the electric field at the position indicated by the dot in (figure 1)? assume that x -axis is horisontal and points to the right, and y -axis points upward.
Velocity in x direction remains constant i.e, vx = 10 m/s Now acceleration is 0.
what are the strength and direction of the electric field at the position indicated by the dot in (figure 1)?
The electric field generated by the positive charge at the dot is directed away from the positive charge. The electric field generated by the negative charge at the dot is directed towards the negative charge.The direction of the electric field due to positive point charge is always acts away from the point charge and electric field due to the negative charge acts towards the negative charge.Because an electric field has both magnitude and direction, the direction of the force on a positive charge is chosen arbitrarily as the direction of the electric field. Because positive charges repel each other, the electric field around an isolated positive charge is oriented radially outward.To learn more about direction refers to:
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Answer these questions please
Atomic theory development, a new model of the atom was created in 1913 by Neils Bohr, a student of Rutherford's.
What progress has been made in the atom model?
According to John Dalton, atoms—which he pictured as little solid balls—are the smallest units of matter. The following concepts were part of Dalton's model: it is impossible to simplify an atom. Every element has the same number of atoms.Atomic theory development, A new model of the atom was created in 1913 by Neils Bohr, a student of Rutherford's. The orbits of the electrons surrounding the nucleus, according to his theory, are circular and concentric. The term "planetary model" refers to this model, which is based on the solar system.Atomic theory development, a new model of the atom was created in 1913 by Neils Bohr, a student of Rutherford's.To learn more about atom model refer to:
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What is the ratio of the magnitude of the electric field at observation point D
to the magnitude of the electric field at observation point C?
The ratio of the magnitude of the electric field at observation point D
to the magnitude of the electric field at observation point C is 16 : 49.
What is electric field?
The electric field strength is the measure of the strength of an electric force per a given unit charge.
E = ( kq ) / ( r² )
where;
k is coulomb's constantr is the distance of the chargeq is the magnitude of the chargeThe position of point c from the center = 4
EC = ( kq ) / ( 4² )
EC = ( kq ) / ( 16 )
The position of point D from the center = 7
ED = ( kq ) / ( 7² )
ED = ( kq ) / ( 49 )
Ratio of electric field at point D to point C is calculated as;
= 16 / 49
= 16 : 49
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A proton is released from rest inside a region of constant, uniform electric field 1 pointing due north.
29.8 s after it is released, the electric field instantaneously changes to a constant, uniform electric field 2 pointing due south. 7.65 s after the field changes, the proton has returned to its starting point. What is the ratio of the magnitude of 2 to the magnitude of 1? You may neglect the effects of gravity on the proton
Answer:
The ratio of the magnitude of 2 to the magnitude of 1 is 1:1
Explanation:
The proton is released in an electric field pointing due north and, 29.8 seconds later, the field changes to a constant, uniform electric field pointing due south. 7.65 seconds after the field changes, the proton has returned to its starting point.
The proton was initially at rest and the electric field caused it to accelerate. The proton's acceleration is directly proportional to the electric field and inversely proportional to its mass.
The proton is acted on by two fields with opposite direction, which means that the net acceleration is zero. Therefore, the ratio of the magnitude of electric field 2 to the magnitude of electric field 1 is 1:1
The ratio of the magnitude of 2 to the magnitude of 1 is 1:1
he cable ade is tied at a and e, and loops through the frictionless loop on the 10 kg mass as shown. cables ab and ac are in the x and z directions, respectively.
The cables AB and AC are in the X and Z directions (See Picture), respectively. Tension in cable ADE will be 98 N.
In physics, tension is defined as the pulling force that is transmitted axially through the use of a string, rope, chain, or similar object, or by the ends of a rod, truss member, or other similar three-dimensional object. Tension can also be defined as the action-reaction pair of forces acting at the ends of the aforementioned elements.
Let us consider the Free body Diagram(See picture).
According to the Free body Diagram, the Point D is in equilibrium.
We know, at Equilibrium condition,
[tex]T-mg=0[/tex]
[tex]T=mg[/tex]
Now, given mass(m) = 10kg, and we know [tex]g=9.8m/sec^{2}[/tex]
[tex]T=10*9.8[/tex]
[tex]T=98N[/tex]
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The complete question is:
The cable ADE is tied at A and E, and loops through the frictionless loop on the 10 kg mass as shown. Cables AB and AC are in the y and x directions, respectively. Use a free body diagram of point D to determine the tension T in cable ADE
which of the following are the characteristics of grounded theory research? (select all that apply).
In the context of society, it focuses upon experiences or processes. b. It always advances theory. A force in qualitative research is grounded theory research.
What does a force mean in science?The term "force" has a defined meaning in science. A energy is not something an object "has in it" or that it "contains." A force is applied to one item by another. Neither live organisms nor inanimate objects are the only things that can be considered forces.
Who are the units of force?The newton, represented by the letter N, is the Standard unit of force. The metre, a unit of length with the sign m, is one of the fundamental units that relate to force. the kilogram
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rank the work done on the cars to create these changes in velocity. be mindful that the sign of the work value matters in the ra
We can say that forces produce changes in velocity because they alter the direction or speed of an object.
What is the name for an alteration in velocity?When an item alters its velocity, it experiences acceleration.Acceleration is the quantity measuring the speed of change. Acceleration is a vector, much like velocity, and it has both a magnitude and a direction. A car moving straight forward, for instance, is said to have forward (positive) acceleration if it is speeding up and rearward (negative) acceleration if it is slowing down.Things move because of forces. They have the power to initiate motion, as well as to slow down, stop, or reverse the motion of an item in motion. We can say that forces produce changes in velocity because they alter the direction or speed of an object.The complete question is,
Why do velocities change?
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figure 6-20 shows an approximate representation of force versus time during the collision of a 56 g tennis ball with a wall. the initial velocity of the ball is 30 m/s perpendicular to the wall; it rebounds with the same speed, also perpendicular to the wall. what is the value of fmax , the maximum contact force during the collision?
The maximum contact force during the collision will be 900 N.
The ball strikes the wall perpendicularly with speed v and rebounds with the same speed.
therefore, a change in momentum
Δp = mv-(-mv) = 2mv
here, m = 56 g and v = 30 m/s
so, Δp = 2x56x10⁻³x30 = 3.36 kgm/s
Now, we have to obtain the impulse so we have to find out the area under the force-time graph
J = Fmax(2ms+6ms)/2
J = Fmax(4ms)
or Fmax = J/(4ms)
or Fmax = Δp/(4ms)
Now, putting the value of Δp
Fmax = [tex]\frac{3.6}{4x10^{-3}}[/tex] = 900 N
Therefore, the maximum contact force during the collision will be 900 N.
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1. What is the volume of a solid aluminum sphere with a diameter of 5 inches? Report in cubic meters.
a. If the density of aluminum is 2,700 kg/m3 what is the mass of the aluminum?
b. How many aluminum atoms are in the sphere?( the stable aluminum isotope is 27Al.)
c. Now suppose we give our aluminum sphere a potential of +100 Volts, this corresponds to a charge of about . How many electrons have been gained/lost?
The volume of solid aluminum sphere is 0.00858 cubic meters and mass is 23.16 kg.
The atomic mass is the mass of an atom. The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The atomic mass is carried by the atomic nucleus, which occupies only about 10-12 of the total volume of the atom or less, but it contains all the positive charge and at least 99.95% of the total mass of the atom. Note that, each element may contain more isotopes, therefore this resulting atomic mass is calculated from naturally-occuring isotopes and their abundance.The volume of sphere is given by formula : [tex]\frac{4}{3} \pi r^{3}[/tex]
Where,
r = radius of sphere
Given, r = 5 inches = 0.127 meters
Putting this value in above equation we get, Volume= 0.00858 cubic meters.
Given density of aluminum is 2700 kg/m^3
We know that:
Density = Mass / Volume
i.e. Mass = Density * Volume
= 2700 kg/m^3 * 0.00858 m^3
= 23.16 kg
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for this trajectory, what would the vertical component of acceleration for the module be at time tm
The vertical component of acceleration at time tm can be determined by taking the second derivative of the vertical position vector with respect to time.
What is velocity?
Velocity is a vector quantity that measures the rate and direction of change in an object's position. It is typically expressed in units of meters per second (m/s). Velocity is equal to the distance traveled divided by the time it takes to travel that distance. Velocity is also related to acceleration, which is the rate of change of velocity.
At time tm, the vertical component of acceleration for the module would be the derivative of the vertical velocity vector with respect to time, which is the change in vertical velocity over time. This can be calculated by taking the second derivative of the vertical position vector with respect to time. Since the position vector is a function of time, the acceleration can be determined by taking the second derivative of the position vector with respect to time, which is defined as the rate of change of the velocity with respect to time. Therefore, the vertical component of acceleration at time tm can be determined by taking the second derivative of the vertical position vector with respect to time.
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I only need question 12 answered
A vector's length is considered to be its magnitude. A is used to represent the vector's magnitude.
A vector's magnitude can be determined in what ways?|v| =(x2 + y2) is the formula to calculate a vector's magnitude in two dimensions, where v = (x, y). From the Pythagorean theorem, this formula was obtained. In three-dimensional space, the formula to calculate a vector's magnitude is V = (x, y, z).A vector's length is considered to be its magnitude. A is used to represent the vector's magnitude. For more details on a vector's magnitude, see to its introduction. On this page, formulas for the magnitude of vectors in two and three dimensions in terms of their coordinates are developed.To learn more about vector's length refer to:
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The angle measured anticlockwise from the +x axis can be used to find vector components as well. In that instance, the x-component and y-component, respectively, will always be cos and sin.
How do you find the x and y components of a vector given velocity?The components of velocity v x=v cos and v y=v sin, where v is the magnitude of the velocity and is its direction in relation to the horizontal, have magnitudes of v x=v cos and v y=v respectively.Fill in a and b in the formula [tex]|v|=a_2+b_2 | v |=a_2 + b_2[/tex] for a vector with the values a and b. Step 2: Underly the square root first, and then simplify the square root as much as you can, to simplify the magnitude[tex]|v|=a_2+b_2 | v |=a_2 + b_2[/tex]. Finding the horizontal component requires multiplying the vector's magnitude by the cosine of the vector's angle, and finding the vertical component requires multiplying the vector's magnitude by the sine of the vector's angle.To learn more about vector refer to :
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A capacitor has an initial charge of 10 µC. It is observed that after discharging for 2ms through a resistor of 8.7 kn, the charge of the capacitor is now only 8.1 μС. What is the capacitance of the capacitor? Express your answer in micro Farad, and keep three significant digits.
The capacitance on the capacitor with initial charge of 10µC is 1.094 μF.
What is Capacitance?Capacitance can be defined as the capability of a material object or any device to store the electric charge. Capacitance is measured by the change in charge in response to the difference in electric potential of an object, it is expressed as the ratio of the quantities.
Initial charge, Q₀ = 10μC
Time, t = 2 ms
1ms = 10⁻³s
t = 2 × 10⁻³s
Resistance, R = 8.7K Ω
1ΚΩ = 10³Ω
R = 8.7 × 10³ Ω
Charge, Q = 8.1 μC
For a discharging RC circuit
Q = Q₀ × [tex]e^{-t/RC}[/tex]
(Q/Q₀) = [tex]e^{-t/RC}[/tex]
8.1/Q = [tex]e^{-0.002/8.7.10^{3}.C }[/tex]
Apply In on both sides,
In(8.1/10) = ln(e⁻2×10⁻³/8.7 × 10³ × C)
ln(0.81) = 2 × 10⁻³/ 8.7 × 10³ × C
-0.210 = 2 × 10⁻³/ 8.7 × 10³ × C
C = 2 × 10⁻³/8.7 × 10³ × 0.210
C = 2 × 10⁻³/ 1.827 × 10³F
C = 1.094 μF
Therefore, the capacitance of the capacitor is 1.094 μF.
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A projectile is shot directly away from Earth's surface. Neglect the rotation of Earth.what multiple of Earth's radius R E
gives the radial distance a projectile reaches if (a) its initial speed is 0.500 of the escape speed from Earth and (b) its initial kinetic energy required to escape Earth (c) what is the least initial mechanical energy required at launch if the projectile is to escape Earth
A projectile is shot directly away from Earth's surface.
Find the multiple of Earth's radius that corresponds to the radial distance a projectile travels if its beginning speed is that of the escape speed from Earth and if its initial kinetic energy is that of the kinetic energy necessary to leave Earth using the concept of energy conservation. Energy cannot be created or destroyed, according to the rule of conservation of energy.
(a)In this question, [tex]V_{0}[/tex] = [tex]\sqrt{GM/2R_{E}}[/tex] is known. Using energy-saving techniques, we have
1/2m[tex]v_{0}^{2}[/tex] - GMm/R = -GMm/r
which is going to yield r = 4[tex]R_{e}[/tex]/3. There fore the multiple of [tex]R_{e}[/tex] is 4/3 or 1.33.
(b)Using the equation, we can see that [tex]K_{i}[/tex]= GMm/2[tex]R_{E}[/tex] exists in this issue, and the aforementioned adjustment (which makes use of energy conservation) results in r= 2[tex]R_{E}[/tex] in this instance. [tex]R_{E}[/tex] is therefore a multiple of 2.00.
(c)We may see from (c) that the mechanical energy is equal to zero.
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Suppose you hold a small ball in contact with, and directly over, the center of a large ball. If you then drop the small ball a short time after dropping the large ball, the small ball rebounds with surprising speed. To show the extreme case, ignore air resistance and suppose the large ball makes an elastic collision with the floor and then rebounds to make an elastic collision with the still-descending small ball. Just before the collision between the two balls, the large ball is moving upward with velocity v
→
and the small ball has velocity -v
→
. (Do you see why?) Assume the large ball has a much greater mass than the small ball.
A. What is the velocity of the small ball immediately after its collision with the large ball?
B. From the answer to part A, what is the ratio of the small ball's rebound distance to the distance it fell before the collision?
We can make a few predictions about the relative velocities prior to and following the impact if kinetic energy and momentum are conserved. Both before and after the impact, the relative velocity is of equal magnitude.
After a collision, how can you determine an object's velocity?If you know the other values of an object's properties, you may determine its momentum or velocity using the momentum equation p = m•v.Despite not being able to move the huge ball very far, the small ball's momentum and velocity will be transferred to it. State the third law of motion of Newton.We can make a few predictions about the relative velocities prior to and following the impact if kinetic energy and momentum are conserved. Both before and after the impact, the relative velocity is of equal magnitude.We can make a few predictions about the relative velocities prior to and following the impact if kinetic energy and momentum are conserved.To learn more about relative velocities refer to:
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